We show some sufficient conditions on a Banach space X concerning the generalized James constant, the generalized Jordan-von Neumann constant, the generalized Zbagănu constant, the coefficient ε̃0 X , the weakly convergent sequence coefficientWCS X , and the coefficient of weak orthogonality, which imply the existence of fixed points for multivalued nonexpansive mappings. These fixed point theor...

As a generalization of Banaś-Fra̧czieck space, the space Xλ ,p that denotes R 2 endowed with the norm ‖x‖λ ,p = max{λ |x1 |,‖x‖p} for λ > 1 , p 1 and x = (x1,x2) ∈ R2 is well defined. In this note, the exact value of the the James type constants JXλ ,p ,t(1) and von Neumann-Jordan constant CNJ (Xλ ,p) about this space for p 2 are investigated.

By the Von Neumann regular graph of R, we mean the graph that its vertices are all elements of R such that there is an edge between vertices x,y if and only if x+y is a von Neumann regular element of R, denoted by G_Vnr (R). For a commutative ring R with unity, x in R is called Von Neumann regular if there exists x in R such that a=a2 x. We denote the set of Von Neumann regular elements by V nr...

We give a simple proof of a characterization of euclidean space due to Aronszajn and derive a well-known characterization due to Jordan & von Neumann as a corollary. A norm || || on a vector space V is euclidean if there is an inner product 〈 , 〉 on V such that ||v|| = √ 〈v,v〉. Characterizations of euclidean normed spaces abound. Amir [1] surveys some 350 characterizations, starting with a well...